Formal Verification with Constrained Polynomial Logical Zonotope

In this paper, we propose using constrained polynomial logical zonotopes for formal verification of logical systems. We perform reachability analysis to compute the set of states that could be reached. To do this, we utilize a recently introduced set representation called polynomial logical zonotopes for performing computationally efficient and exact reachability analysis on logical systems. Notably, polynomial logical zonotopes address the "curse of dimensionality" when analyzing the reachability of logical systems since the set representation can represent 2^n binary vectors using n generators. After finishing the reachability analysis, the formal verification involves verifying whether the intersection of the calculated reachable set and the unsafe set is empty or not. However, polynomial logical zonotopes are not closed under intersections. To address this, we formulate constrained polynomial logical zonotopes, which maintain the computational efficiency and exactness of polynomial logical zonotopes for reachability analysis while supporting exact intersections. Furthermore, we present an extensive empirical study illustrating and verifying the benefits of using constrained polynomial logical zonotopes for the formal verification of logical systems.